Graphing Calculator Investigation
A Middle School Lesson
Submitted by Kathy Hill
The Mathematics: Functional relationships can be expressed in real contexts, graphs, algebraic equations, tables and words.
The task: Use a graphing calculator to graph sets of equations and look for similarities.
Materials: graphing calculator
The Lesson:
Before the task (introducing)
1. Give students calculators to “play” with.
2. Have students make a T-chart and sketch a graph for the equation y = 2x. Press the Y= button and enter the equation into the calculator. Press the graph button. Experiment with the numbers in the window to get a graph that looks like the one they sketched. Ask, “What have you discovered that gives you a window you like?”
3. Press Table button. Compare table on calculator to the T-chart. Press table set button and practice setting table parameters. Practice by asking:
If x = 2, what is y? (4)
If x = 2/3, what is y? (4/3)
If x = 3.25, what is y? (6.5)
If x = 527, what is y? (1054)
4. Introduce task. “Experiment with your graphing calculator and these equations (on worksheet). Graph one set of equations at a time. For each set, two of the graphs will be similar in some way and one of the graphs will be different. Sketch what you see on your calculator screen. Answer questions A and B for each set.”
During the task
Questions to ask
- Are your plots off?
- What scale are you using in your window? Does it match the scale of your sketch?
- Which equation goes with which graph?
- How are the equations similar? How are the graphs similar?
- What do you think the T-chart of this equation will look like?
After the task (summarizing)
1. Put students in groups of 3-4 to discuss answers to the questions and share their sketches.
2. Whole group discussion: “What new thing did you learn?”
Using the Graphing Calculator Investigation
Experiment with your graphing calculator and these equations. Graph one set of equations at a time. For each set, two of the graphs will be similar in some way and one of the graphs will be different. Sketch what you see on your calculator screen. Answer questions A and B for each set.
Set 1:y = 3x – 4y = x2y = 3x + 2
Set 2:y = 5y = 3xy = 1x
Set 3: y = 2x + 3y = 2x – 5y = 0.5x + 2
Set 4:y = 2xy = 2 ÷ xy = x + 5
A. Which two equations in the set have graphs that are similar?
In what ways are the two graphs similar?
In what ways are the equations for the two graphs similar?
B. Which equation in the set has a graph that is different from the graphs of the other equations?
In what way is the graph different from the other graphs?
In what way is the equation different from the other equations?